Comprehensive Revision Notes: Coordination Compounds

1. Introduction and Core Definitions

• Coordination Compounds: These are complex compounds in which transition metal atoms or ions are bound to a fixed number of anions or neutral molecules by sharing of electrons. Unlike double salts, these compounds retain their identity in solid as well as in solution form.

• Coordination Entity: A central metal atom or ion bonded to a fixed number of ions or molecules enclosed within square brackets. For example, in $[CoCl_3(NH_3)_3]$, the cobalt ion forms the coordination entity with three ammonia molecules and three chloride ions.

• Central Atom/Ion: The atom or ion in a coordination entity to which a fixed number of ligands are bound in a definite geometrical arrangement. Because they accept electron pairs, central metal atoms or ions act as Lewis acids.

• Ligands: The ions or molecules bound to the central atom or ion in a coordination entity. They act as Lewis bases by donating electron pairs. They are classified based on denticity (the number of donor atoms):

  • Unidentate: Bound through a single donor atom (e.g., $Cl^-$, $H_2O$, $NH_3$).

  • Didentate: Can bind through two donor atoms simultaneously (e.g., oxalate $C_2O_4^{2-}$, ethane-1,2-diamine abbreviated as 'en').

  • Polydentate: Contain multiple donor atoms present in a single ligand. For example, Ethylenediaminetetraacetate ion ($EDTA^{4-}$) is an important hexadentate ligand that binds through two nitrogen and four oxygen atoms.

  • Chelate Ligand & Chelate Effect: When a di- or polydentate ligand uses two or more donor atoms simultaneously to bind to a single metal ion, it forms a ring-like structure called a chelate. Chelate complexes tend to be exceptionally more stable than similar complexes containing unidentate ligands.

  • Ambidentate Ligands: Unidentate ligands that possess two different donor atoms and can coordinate through either of the two sides (e.g., $NO_2^-$ can coordinate as $-NO_2$ via nitrogen or $-ONO$ via oxygen; $SCN^-$ can coordinate via sulfur or nitrogen).

• Coordination Number (CN): The total number of ligand donor atoms to which the metal ion is directly bonded via sigma bonds. Pi bonds formed between the ligand and central metal are not counted for this purpose.

• Coordination Sphere and Counter Ions: The central atom/ion and its attached ligands are collectively enclosed in square brackets, forming the non-ionisable coordination sphere. The ionisable groups written outside the square brackets are called counter ions.

• Coordination Polyhedron: The spatial arrangement of the ligand donor atoms directly attached to the central metal atom/ion defines a specific geometric shape, such as octahedral, tetrahedral, or square planar.

• Homoleptic and Heteroleptic Complexes: Complexes bound to only one kind of donor ligand group (e.g., $[Co(NH_3)_6]^{3+}$) are homoleptic, while those bound to more than one kind of donor ligand group (e.g., $[Co(NH_3)_4Cl_2]^+$) are heteroleptic.

2. Double Salts vs. Coordination Complexes

• Double Salts: These are formed by the combination of two or more stable salts in a stoichiometric ratio and completely dissociate into simple individual constituent ions when dissolved in water. Examples include Carnallite ($KCl\cdot MgCl_2\cdot 6H_2O$), Mohr's salt ($FeSO_4\cdot (NH_4)_2SO_4\cdot 6H_2O$), and Potash alum ($KAl(SO_4)_2\cdot 12H_2O$).

• Coordination Complexes: These compounds also combine stable entities but do not dissociate into simple simple constituent ions completely in solution. For example, $K_4[Fe(CN)_6]$ dissociates to yield $K^+$ and the intact complex ion $[Fe(CN)_6]^{4-}$, without liberating free $Fe^{2+}$ or $CN^-$ ions.

3. Werner's Theory of Coordination Compounds

Alfred Werner formulated the foundational theory of coordination chemistry based on two types of valences displayed by metal ions:

1. Primary Valence: This valence is ionisable, corresponds to the oxidation state of the metal ion, and is satisfied strictly by negative ions.

2. Secondary Valence: This valence is non-ionisable, corresponds directly to the fixed coordination number of the metal, and is satisfied by either neutral molecules or negative ions.

3. Spatial Orientation: The ligands satisfying the secondary valences have directional properties and are arranged in specific, characteristic spatial arrangements (coordination polyhedra) around the metal.

Experimental Validation via Precipitation:

By adding excess cold silver nitrate ($AgNO_3$) solution to various cobalt(III) chloride-ammonia complex variants, the moles of $AgCl$ precipitated per mole of complex help deduce the structural formula:

In the textbook, the formulation and structural behavior of the cobalt(III) chloride–ammonia complex series serve as the foundational proof for Alfred Werner's coordination theory.

Werner prepared a series of addition compounds by combining cobalt(III) chloride ($CoCl_3$) with different amounts of ammonia ($NH_3$). To understand their true structures, he conducted simple precipitation experiments using cold, excess silver nitrate ($AgNO_3$) solution along with solution conductivity measurements.

1. Experimental Observations

When 1 mole of each complex was reacted with excess cold $AgNO_3$ solution, the number of moles of white silver chloride ($AgCl$) precipitated varied across the series:

• $\text{CoCl}_3 \cdot 6\text{NH}_3$ (Yellow color): Precipitated 3 moles of $AgCl$.

• $\text{CoCl}_3 \cdot 5\text{NH}_3$ (Purple color): Precipitated 2 moles of $AgCl$.

• $\text{CoCl}_3 \cdot 4\text{NH}_3$ (Green color): Precipitated 1 mole of $AgCl$.

• $\text{CoCl}_3 \cdot 4\text{NH}_3$ (Violet color): Precipitated 1 mole of $AgCl$.

2. Werner’s Explanation and Formulation

Werner deduced that for every complex in this series, the central cobalt ion ($Co^{3+}$) always maintains a fixed secondary valence (coordination number) of 6. This means exactly six groups—whether they are ammonia molecules, chloride ions, or a mix of both—must be tightly bound directly to the cobalt ion.

These directly attached groups form the non-dissociating coordination sphere and are written inside square brackets $[ \ ]$. Any chloride ions not required inside the sphere are left outside as ionisable counter ions to satisfy the primary valence.

Based on this principle, the complexes are formulated as follows:

In coordination chemistry, the electrolyte designations mentioned in the table (1:3, 1:2, and 1:1 electrolytes) refer to the stoichiometric ratio of the complex ion to the counter ions produced in a solution when one formula unit of the compound completely dissociates.

This classification tells us how many free ions are released in water, which directly dictates the solution conductivity of that specific coordination compound.

1. 1:3 Electrolyte

• Meaning: One formula unit of the complex dissociates to yield one complex cation and three counter anions.

• Example from Table: The yellow compound, formulated as $[Co(NH_3)_6]Cl_3$.

• Dissociation Reaction:

  $[Co(NH_3)_6]Cl_3 \xrightarrow{\text{water}} \underbrace{1 \ [Co(NH_3)_6]^{3+}}_{\text{1 Complex Cation}} + \underbrace{3 \ Cl^-}_{\text{3 Counter Anions}}$

• Conductivity Behavior: It yields a total of 4 free ions in solution. Because it produces the highest total number of mobile ions and a high $+3$ charge on the complex cation, it exhibits the highest solution conductivity in this series.

2. 1:2 Electrolyte

• Meaning: One formula unit dissociates to yield one complex cation and two counter anions.

• Example from Table: The purple compound, formulated as $[CoCl(NH_3)_5]Cl_2$.

• Dissociation Reaction:

  $[CoCl(NH_3)_5]Cl_2 \xrightarrow{\text{water}} \underbrace{1 \ [CoCl(NH_3)_5]^{2+}}_{\text{1 Complex Cation}} + \underbrace{2 \ Cl^-}_{\text{2 Counter Anions}}$

• Conductivity Behavior: It yields a total of 3 free ions in solution. Its electrical conductivity is intermediate—lower than the 1:3 electrolyte but higher than a 1:1 electrolyte.

3. 1:1 Electrolyte

• Meaning: One formula unit dissociates to yield exactly one complex cation and one counter anion.

• Examples from Table: The green and violet structural isomers, both formulated as $[CoCl_2(NH_3)_4]Cl$.

• Dissociation Reaction:

  $[CoCl_2(NH_3)_4]Cl \xrightarrow{\text{water}} \underbrace{1 \ [CoCl_2(NH_3)_4]^+}_{\text{1 Complex Cation}} + \underbrace{1 \ Cl^-}_{\text{1 Counter Anion}}$

• Conductivity Behavior: It yields a total of only 2 free ions in solution. Consequently, it has the lowest electrical conductivity among the listed complexes because it releases the fewest ions and carries the lowest charge magnitude.

3. Key Concepts Illustrated by this Series

• Dual Behavior of Chloride Ions: In $[Co(NH_3)_6]Cl_3$, all three $Cl^-$ ions act purely as counter ions (satisfying primary valence) and completely precipitate out. However, as the number of available ammonia molecules drops (e.g., in $[CoCl_2(NH_3)_4]Cl$), some chloride ions are forced inside the square brackets to keep the coordination number at 6. These interior chloride ions satisfy both primary and secondary valences, becoming non-ionisable and trapped during the precipitation reaction.

• Discovery of Isomerism: The last two compounds share the identical empirical formula ($CoCl_3 \cdot 4NH_3$) but exhibit totally different colors (Green and Violet) and properties. Werner recognized that these distinct properties arise because the atoms have different spatial orientations around the metal, giving birth to the concept of isomers in coordination chemistry.

4. IUPAC Nomenclature and Formulas

Rules for Writing Formulas:

• The central metal atom is always listed first inside the square brackets.

• Ligands are listed next in strictly alphabetical order, completely irrespective of their electric charges.

• Polyatomic ligands or abbreviated ligand indicators are enclosed in parentheses.

• No spaces are left between the ligands and the central metal within the coordination sphere.

Rules for Systematic Naming:

• The cation is always named first, whether it is a simple ion or the complex ion entity.

• Within the complex ion, ligands are named in alphabetical order before the name of the central metal.

• Anionic ligands end with the suffix -o or -ido (e.g., chlorido, cyanido, oxalato). Neutral ligands retain their standard elemental name except for specific allocations: $H_2O$ is named aqua, $NH_3$ is named ammine, $CO$ is named carbonyl, and $NO$ is named nitrosyl.

• Multipliers di-, tri-, tetra- indicate ligand counts. If the ligand name already contains a numerical prefix, prefixes like bis-, tris-, tetrakis- are utilized, with the ligand name placed inside parentheses.

• The oxidation state of the metal is explicitly specified using a Roman numeral enclosed in parentheses right after the metal's name.

• Central Metal Ending: If the complex is a cation or neutral, the metal retains its elemental name. If the complex is an anion, the metal name must end with the suffix -ate (e.g., cobaltate, chromate, zincate), often reverting to its Latin stem (e.g., ferrate for iron, argentate for silver).

5. Isomerism in Coordination Compounds

Isomers share the same overall chemical formula but feature differing atomic arrangements, imparting distinct physical or chemical properties.

                         Isomerism
                             |
         -----------------------------------------
        |                                         |
 Stereoisomerism                           Structural Isomerism
        |                                         |
   -- Geometrical Isomerism                  -- Linkage Isomerism
  |                                         |
   -- Optical Isomerism                      -- Coordination Isomerism
                                            |
                                             -- Ionisation Isomerism
                                            |
                                             -- Solvate Isomerism

A. Stereoisomerism

Stereoisomers share identical chemical formulas and bonding linkages but possess completely different spatial orientations.

• Geometrical Isomerism: Arises in heteroleptic complexes due to different geometric position arrangements of the ligands:

  • Square Planar Complexes ($CN=4$): Complexes of type $[MX_2L_2]$ show cis-isomerism when identical ligands occupy adjacent positions, and trans-isomerism when they sit directly opposite to each other.

  • Octahedral Complexes ($CN=6$): Complexes of type $[MX_2L_4]$ exhibit cis- and trans- orientations. Complexes of type $[Ma_3b_3]$ (e.g., $[Co(NH_3)_3(NO_2)_3]$) display facial (fac) isomerism when three identical donor atoms occupy adjacent positions on an octahedral face, and meridional (mer) isomerism when they span the meridian line.

  • Note: Tetrahedral complexes never show geometrical isomerism because all four coordination positions are perfectly equivalent relative to one another.

• Optical Isomerism: Occurs when structural mirror images are non-superimposable on one another. These non-superimposable chiral structural mirror images are called enantiomers. The form that rotates plane-polarized light to the right is the dextro ($d$) isomer, and the one rotating it to the left is the laevo ($l$) isomer. This behavior is common in octahedral complexes containing didentate ligands, where only the cis- form of heteroleptic structures remains chiral.

B. Structural Isomerism

Structural isomers have different chemical bonds and connectivity arrangements:

• Linkage Isomerism: Occurs when an ambidentate ligand binds to the central metal atom via different donor atoms (e.g., $[Co(NH_3)_5(NO_2)]Cl_2$ is yellow when bound through nitrogen, and red when bound through oxygen as $-ONO$).

• Coordination Isomerism: Arises from the complete interchange of ligands between the cationic and anionic complex entities present within a salt combination (e.g., $[Co(NH_3)_6][Cr(CN)_6]$ vs. $[Cr(NH_3)_6][Co(CN)_6]$).

• Ionisation Isomerism: Occurs when the counter ion in a complex salt replaces a ligand inside the coordination sphere, changing the ions liberated in solution (e.g., red-violet $[Co(NH_3)_5(SO_4)]Br$ yields a $Br^-$ precipitate, while red $[Co(NH_3)_5Br]SO_4$ yields a $BaSO_4$ precipitate with $Ba^{2+}$).

• Solvate / Hydrate Isomerism: Differs by whether a solvent molecule (typically water) is directly bound to the metal atom as a ligand or occupies a free space in the crystal lattice (e.g., violet $[Cr(H_2O)_6]Cl_3$ vs. grey-green $[Cr(H_2O)_5Cl]Cl_2\cdot H_2O$).

6. Bonding Theories in Coordination Compounds

A. Valence Bond Theory (VBT)

VBT postulates that a central metal atom or ion, under the strong influence of incoming ligands, hybridises its valence $(n-1)d, ns, np$, or $nd$ atomic orbitals to form a set of equivalent vacant orbitals matching its coordination number. These vacant hybridised orbitals then overlap with filled ligand orbitals to accept donated electron pairs.

• Inner vs. Outer Orbital Complex: When the inner $(n-1)d$ orbitals participate in hybridisation ($d^2sp^3$), it forms an inner orbital or low spin/spin-paired complex. When outer $nd$ orbitals are utilized instead ($sp^3d^2$), it yields an outer orbital or high spin/spin-free complex.

• Limitations of VBT: It involves many assumptions; fails to give a quantitative interpretation of magnetic data; does not explain the origin of colors exhibited by complexes; and cannot distinguish between weak and strong field ligands.

B. Crystal Field Theory (CFT)

CFT is an electrostatic model that views the metal-ligand bond as purely ionic, arising solely from electrostatic attractions between the positive metal ion and negative point charges (anions) or point dipoles (neutral molecules).

In a free gaseous metal atom, all five $d$ orbitals are degenerate (equal in energy). When a negative ligand field approaches, this degeneracy is lifted, splitting the $d$ orbitals into distinct energy levels depending on the geometry:

1. Octahedral Splitting ($\Delta_o$):

• Ligands approach directly along the axes ($x, y, z$). Orbitals directed along these axes ($d_{x^2-y^2}$ and $d_{z^2}$) experience greater electrostatic repulsion and are raised in energy to form the $e_g$ set. Orbitals pointing between the axes ($d_{xy}, d_{yz}, d_{xz}$) experience less repulsion and drop in energy to form the $t_{2g}$ set.

• The energy of the two $e_g$ orbitals increases by $\frac{3}{5}\Delta_o$ ($+0.6\Delta_o$), while the energy of the three $t_{2g}$ orbitals decreases by $\frac{2}{5}\Delta_o$ ($-0.4\Delta_o$) relative to the spherical barycenter.

2. Tetrahedral Splitting ($\Delta_t$):

• The splitting pattern is completely inverted because ligands approach between the axes. The $d_{xy}, d_{yz}, d_{xz}$ orbitals are raised to higher energy levels, while the $d_{x^2-y^2}$ and $d_{z^2}$ orbitals drop to lower levels.

• For the same metal and ligands, the splitting energy is much smaller: $\Delta_t = \frac{4}{9}\Delta_o$. Consequently, the splitting energy is rarely large enough to force electron pairing, so tetrahedral complexes are almost always high spin. Because tetrahedral shapes lack a center of inversion symmetry, the subscript 'g' is omitted.

Spectrochemical Series:

Ligands are arranged in an experimentally determined series based on their ability to split the $d$ orbitals:

I^- < Br^- < SCN^- < Cl^- < S^{2-} < F^- < OH^- < C_2O_4^{2-} < H_2O < NCS^- < EDTA^{4-} < NH_3 < en < CN^- < CO

Filling of $d$-orbitals for $d^4$ to $d^7$ ions:

The distribution of electrons depends on the relative magnitudes of the crystal field splitting energy ($\Delta_o$) and the pairing energy ($P$, the energy required to pair two electrons in a single orbital):

• Weak Field Ligands (\Delta_o < P): The splitting is small. The fourth electron avoids pairing by entering the higher $e_g$ level, giving a $t_{2g}^3 e_g^1$ configuration. This results in a high spin complex.

• Strong Field Ligands ($\Delta_o > P$): The splitting is large. It is more energetically favorable for the fourth electron to pair up in the lower $t_{2g}$ level, giving a $t_{2g}^4 e_g^0$ configuration. This results in a low spin complex.

Colour in Coordination Complexes:

• Color arises from $d-d$ electronic transitions. When an electron in a lower $t_{2g}$ orbital absorbs light from the visible spectrum, it is excited to an empty higher $e_g$ level. The complex then transmits the remaining light, displaying the complementary color of the absorbed wavelength.

• For example, $[Ti(H_2O)_6]^{3+}$ is a $3d^1$ system where the single electron sits in the $t_{2g}$ level in the ground state. It absorbs blue-green light to excite the electron to the $e_g$ level, making the complex appear violet.

• Crucial Note: In the absence of ligands, crystal field splitting does not occur, and the substance remains colorless (e.g., heating blue hydrated $CuSO_4\cdot 5H_2O$ removes its water ligands, turning it into white anhydrous $CuSO_4$).

7. Bonding in Metal Carbonyls

• Most transition metals form homoleptic metal carbonyls, such as tetrahedral $[Ni(CO)_4]$, trigonal bipyramidal $[Fe(CO)_5]$, and octahedral $[Cr(CO)_6]$.

• The metal-carbon bond in these carbonyls possesses both $\sigma$ (sigma) and $\pi$ (pi) character, creating a synergic effect that strengthens the overall linkage:

  1. $\sigma$-bond component: Formed by the donation of a lone pair of electrons from the carbonyl carbon atom into a vacant orbital on the central metal.

  2. $\pi$-bond component: Formed by the back-donation of a pair of electrons from a filled $d$ orbital on the metal into the vacant, empty antibonding $\pi^*$ molecular orbital of the carbon monoxide ligand.

8. Importance and Applications of Coordination Compounds

• Analytical Chemistry: Used in qualitative and quantitative analysis through specific color reactions with chelating reagents like $EDTA$, dimethylglyoxime ($DMG$), and $\alpha$-nitroso-$\beta$-naphthol. For example, water hardness is measured by titrating $Ca^{2+}$ and $Mg^{2+}$ ions with standard $Na_2EDTA$.

• Metallurgy and Extraction: Gold and silver are extracted by forming soluble cyano complexes ($[Au(CN)_2]^-$), which are then reduced with zinc metal. Metals are also purified via volatile complex intermediates, such as converting impure nickel to volatile $[Ni(CO)_4]$ and decomposing it to yield pure nickel (Mond's Process).

• Biological Systems: Coordination complexes play vital roles in nature:

  • Chlorophyll: A magnesium coordination complex responsible for plant photosynthesis.

  • Haemoglobin: An iron coordination complex that serves as the oxygen carrier in blood.

  • Vitamin $B_{12}$: A cobalt coordination complex that acts as the anti-pernicious anemia factor.

  • Enzymes: Biocatalysts like carboxypeptidase A and carbonic anhydrase incorporate coordinated metal active sites.

• Industrial Catalysis: Organometallic complexes serve as industrial catalysts; for example, the rhodium complex $[(Ph_3P)_3RhCl]$, known as Wilkinson's Catalyst, is used for the homogeneous hydrogenation of alkenes.

• Medicine & Chelation Therapy: Used to treat heavy metal poisoning, such as using $EDTA$ to remove excess lead from the body. In cancer treatment, the coordination complex cis-platin ($cis-[PtCl_2(NH_3)_2]$) is widely used to inhibit tumor growth.